Related papers: Shearlets and Optimally Sparse Approximations
Sparse structure learning in high-dimensional Gaussian graphical models is an important problem in multivariate statistical signal processing; since the sparsity pattern naturally encodes the conditional independence relationship among…
Image patch matching, which is the process of identifying corresponding patches across images, has been used as a subroutine for many computer vision and image processing tasks. State -of-the-art patch matching techniques take image patches…
Convexity prior is one of the main cue for human vision and shape completion with important applications in image processing, computer vision. This paper focuses on characterization methods for convex objects and applications in image…
We describe an apparatus for subgradient-following of the optimum of convex problems with variational penalties. In this setting, we receive a sequence $y_i,\ldots,y_n$ and seek a smooth sequence $x_1,\ldots,x_n$. The smooth sequence needs…
We present an image preprocessing technique capable of improving the performance of few-shot classifiers on abstract visual reasoning tasks. Many visual reasoning tasks with abstract features are easy for humans to learn with few examples…
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…
Low-rank matrix approximation (LRMA) is a powerful technique for signal processing and pattern analysis. However, its potential for data compression has not yet been fully investigated in the literature. In this paper, we propose sparse…
The approximation of tensors is important for the efficient numerical treatment of high dimensional problems, but it remains an extremely challenging task. One of the most popular approach to tensor approximation is the alternating least…
We propose a novel approximation hierarchy for cardinality-constrained, convex quadratic programs that exploits the rank-dominating eigenvectors of the quadratic matrix. Each level of approximation admits a min-max characterization whose…
We provide the construction of a set of square matrices whose translates and rotates provide a Parseval frame that is optimal for approximating a given dataset of images. Our approach is based on abstract harmonic analysis techniques.…
In this paper, we introduce an end-to-end framework for video analysis focused towards practical scenarios built on theoretical foundations from sparse representation, including a novel descriptor for general purpose video analysis. In our…
The shape of liquid droplets in air plays an important role in aerodynamic behavior and combustion dynamics of miniaturized propulsion systems such as microsatellites and small drones. Their precise manipulation can yield optimal efficiency…
Expand-and-sparsify representations are a class of theoretical models that capture sparse representation phenomena observed in the sensory systems of many animals. At a high level, these representations map an input $x \in \mathbb{R}^d$ to…
This paper deals with near-best approximation of a given bivariate function using elements of quarkonial tensor frames. For that purpose we apply anisotropic tensor products of the univariate B-spline quarklets introduced around 2017 by…
Surrogate models are used to alleviate the computational burden in engineering tasks, which require the repeated evaluation of computationally demanding models of physical systems, such as the efficient propagation of uncertainties. For…
Sparse models for high-dimensional linear regression and machine learning have received substantial attention over the past two decades. Model selection, or determining which features or covariates are the best explanatory variables, is…
Sparse codes in neuroscience have been suggested to offer certain computational advantages over other neural representations of sensory data. To explore this viewpoint, a sparse code is used to represent natural images in an optimal control…
Many biological learning systems such as the mushroom body, hippocampus, and cerebellum are built from sparsely connected networks of neurons. For a new understanding of such networks, we study the function spaces induced by sparse random…
The representation of images in the brain is known to be sparse. That is, as neural activity is recorded in a visual area ---for instance the primary visual cortex of primates--- only a few neurons are active at a given time with respect to…
Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom…